*Disclaimer* This is just my opinion, and we all know what opinions are like...
First - a bulldog is a bulldog and AKC has set a standard for the breed. There are 2 ways to produce a mini of any breed:
- Mix the desired breed with a similar but smaller breed to produce a smaller and nearly identical looking dog to the desired breed.
- Find smaller sized desired breed dogs and breed them together, until you reach a size you are aiming for.

The first option is not desired, and can introduce traits (non-standard fur coloring, eye coloring, etc...) into the desired breed line, that do not fall within bulldog standards. And should never be AKC registered as a pure bulldog.
The second option may take longer, but keeps the bulldog "pure" to the bulldog line.
That being said, no matter what path is used, if the dog is bred to anything outside of the AKC standards, then it is not an AKC Bulldog. With option 2, it may be a bulldog through and through, but it is not an AKC bulldog, and should not be AKC papered... that however, would depend on the integrity of the breeder, and the breed knowledge of the buyer.
Just because a bulldog does not fall into the standard that AKC has set, does not mean it's not a bulldog, it just means that it is not going to be recognized as a bulldog breed by AKC for showing or breeding. As far as cost for a non-standard breed - I guess that would depend on what the market will bear, and what someone is willing to pay at the time.
If I found a "mini" bulldog (not cross bred with another breed) that did not meet the AKC standards, and it had a perfect disposition and fit into my home environment - I would absolutely give it a permanent home! But I am not a breeder, and only have dogs for added family members. :D
I hope I did not offend anyone, just my